- Email: [email protected]
Optimal Estimation of the Range for Mobile Robots Using Ultrasonic Sensors
Copyright Cl IFAC Intelligent Components and Instruments for Control Applications, Annecy, France, 1997
OPTIMAL ESTIMATION OF THE RANGE FOR MOBILE ROBOTS USING ULTRASONIC SENSORS
H. Hamadene and E. CoDe
CEMIF systemes complexes 40, rue du Pelvoux 91020 Evry Cedex hamadene@Cemifuniv-evryjr
Abstract: The measure of the range by an ultrasonic system is based on the measurement of the Time Of Flight (TOF) of an ultrasonic wave between a transmitter and a receiver. According to the signal-to-noise ratio, the TOF accuracy and the range accuracy will depend on the estimation method of the TOF. Three approaches can b~ used according to the complexity : thresholding, suboptimal method and correlation. The correlation method and its ~plementation are described. Simulation and experimental results.
detecting echoes in the received signal the distance between the transducer and the target can be found. But with conventional ultrasonic sensors (Audenaert, et al., 1992), some disadvantages appear because the measured distance depends on amplitude of the echo. Thus weaker echoes will be detected at a later time than stronger ones. This problem can be overcame by using some radar techniques (Berkowitz, 1965). It consists in: - having the estimated distance independent of the echo amplitude. - using an optimal filter in order to optimize the signal-to-noise ratio. - choosing the emitted signal to optimize the resolution.
I . INTRODUCTION
To move in an unknown environment, mobile robots need information given by exteroceptive sensors. The cost and the easiness of implementation explain the great use of ultrasonic sensors to provide range data. But the medium range accuracy and the wide beam complicate the environment recognition. The improvement of recognition ability requires a more accurate range measure. The paper focuses on the contribution of the correlation to the improvement of ultrasonic sensor range accuracy. After introducing briefly optimal filter theory and the three methods of TOF estimation., the corrdator is described. One of the most important point concerns the transmitted signal waveform. The results of simulations and experiments show the advantages of that optimal method compared to the usual thresholding.
The sensor-environment model adopted is the Kuc model (1994) which assumes that a process is linear and the received signal is expressed by r(/)
2. THEORY
=J[htr / ree (t)* helTVlr. (t)] . x(t -
,)d,
r(/ ) = J(htr / ree(t)* x(t)] . henvir(t - ,)dr
r(t) = Jxe(t)ehl /Vir . (t - r)dr (I)
Generally the ultrasonic transducer acts as both transmitter and receiver. It emits a burst of a certain fixed frequency (50 Khz in general which corresponds to the resonance frequency of the transducer), and by 137
Thus the output signal may (Audenaert, et al., 1992) by:
be
3.2. Suboptimal method
represented
r(t)=a.xe(t)+n(t) (2)
For nearby objects, in a high signal-ta-noise ratio case, the time of flight must be estimated by faster methods. It consists in approximating the leading part of the received signal by a function such a parabola (Barshan and Kuc, 1992; Hamadene and Colle 1996a). This is an intermediate approach between the biased threshold and the optimum correlation estimator method described next.
where a is an amplitude factor, Xe(t) is the ultrasonic transmit wave and n(t) is the additive noise present in the signal. In radar theory a filtered signal which has an optimal signal-ta-noise ratio can be expressed by :
y(t) =Jr(t) . h(t - -r)(iT (3) where h(t) is the impulse response of the environment (see equation 1). Such a filter is called a matched filter and its output will be :
3.3. Optimum correlation method A bat echolocation has been anaIyzed by Elfes (1985), he applied optimum correlation detection for TOF binaural estimation and target location. This method employs a matched filter that contains a copy of the echo to determine its location in the observed signal. It is an unbiased estimator which maximises the signal-to noise ratio. However this procedure is time consuming.
where tF is the time of flight of the transmitted pulse, is the time for which the filtered signal y(t) has the largest signal-to noise ratio of all linear filters, and Rx(t) is the autocorrelation function of x(t). By searching the maximum of y(t), the time-of-flight is carried out first and then the distance between the sensor and the target. t~
4. CORRELATOR IMPLEMENTATION 3." TIME-OF-FLIGHT ESTIMATION
The correlator is a digital matched filter in which the correlation is applied essentially between the input (transmitted wave) and the output (reflected wave) fig 1. The received signal is amplified before correlation and then correlated as follow :
The sensor operates in the pulse/echo mode, and acts as both a transmitter and a receiver. The echo reflected from an object may be detected by the same sensor now working as a receiver. Because of the addition of noise to the echoes detected, the TOF needs to be estimated. Three different methods of TOF estimation are presented.
y('t) =
KT
ex•r('t) = -ToJxe(t)·r(t)dt
(6)
where k is an amplification factor and T the duration of the calculus The matched filter can be approximated by a digital finite impulse response (7). The samples are multiplied by coefficients representing discrete samples of the 'reference signal' which is the transmit signal in our case. A mathematical representation of the matched filtering operation is as follows.
3.1. Simple thresholding method The method most frequently used by conventional sensors and sonar ranging systems for extracting the TOF information is a simple thresholding detection (Biber, et al., 1990). The sensor provides a range value when the echo amplitude exceeds a prespecified threshold level 1: which is set according to the noise level cr in order to suppress spurious readings. The time at which the received signal crosses the threshold 1: is denoted by :
N
y(n) = I,xe(i)·r(n-i) (7) ;=0
Note that it is about the cross-correlation and not the autocorrelation function because of the deformations of the received signal due to the reflectors and the finite bandwidth of the transducer. Fig 1 Synoptic of the treatment
r(t)
nX!
L--_--..,~!
where tF is the true value of the TOF, 1: the threshold and !IQ the shape parameter of the envelope of the received signal. The problem inherent to this method is the estimator bias.
~
y(1:)=Cxr('t) ~----~y------~~
correlator
138
Thanks to the amplitude of the filtered output we can get two information: the range r , between the sensor and the object, and its orientation (Hamadene and Colle, 1996b). Some researches are done in the determination of the emitted signal in order to get the correlated output assimilated to the Dirac pulse. This method will enhance the resolution and the signal-to-noise ratio of the sensor.
The emitted signal x(t) is a PSK (phase-Shift Keying) modulation of the Barker code where the carrier is a square wave with a 50 Khz frequency. With the modulation, the maximum level of the spectrum is centered at 50 Khz, the resonance frequency of the transducer. The total length of the emitted signal is 1 ms (polaroid Corporation, 1984), the duration symbol T=4x20~s where 20~s is the period of the carrier signal. Therefore the number of bits in the code must be 13 and B={+I, +1, +1, +1, +1, -1, -1, +1, +1, -1, +1, -1, +1} (Audenaert, et al., 1992; Peremans, et al. 1993).
5. CHOICE OF THE TRANSMIT WAVEFORM It consists in determining a code for which the sequence is as short as possible and its autocorrelation function close to the Dirac pulse. In the following paragraph we describe two kinds of codes and argue ourcboice.
5.2. PNcode Let C={cl' ~, ... , cp } be a sequence of the PN code, this code can easily be obtained by shift registers. For N registers, for example, the sequence generated will have 2N_l values ci= ±1, and the duration signal is (2N_l)T, where T is the duration of each symbol (equation 8). Each ci is evaluated using a characteristic polynome P(x). N was chosen to be 4. By comparing these two codes, one verifies that the length signal in the Barker code is 13T when in PN code it is 15T, also the blind zone of the sensor will be reduced in the Barker code, and the peaklside lobe ratio is 1311 in the Barker code when it is only 8/2 in PN codes figure 2 and figure 3.
5. J Barker code Let B={b l , b 2, .. ,bj, ..,bn } be an n-bits codeword with bi = ±l. From each bit hi a signal waveform can be derived by modulating a carrier signal xb(t) with the respective bi . For each bit bi corresponds a part of the signal x(t), called a symbol.
x(t+(i-l)1)=bi ·xb (t), t E[O,T] (8) where T is the duration of each symbol. 14r--~--~-~--~-----,
12
6. PEAK DETECTION 10
When an object is present in the active region of the ultrasonic range finder, the sensor will receive an echo. The received signal is sampled and converted with a 8 bits AID converter, the sampling period Ts=TC/4=5~s, where Tc is the period of the carrier signal.
4
:-----7-5 ---:'.:10,----~15;:----.:20:";:-----:!25
-20
The numerical received signal is correlated with the transmitted one. Then an evaluation of the absolute value of the filtered signal is made. The determination of the maximum provides the time of flight.
Fig 2 The Auto Correlation Function (ACF) of a 13-bits Barker code 8 7
The estimated results are obtained by simulating the ultrasonic sensors with a physically based model (Kuc and Siege~ 1987) that describes the transducer reflections from plans and corners. The TIR radius is chosen to be 15 mm, identical to the Polaroid transducer. The threshold level is chosen relatively to the amplitude of the echo from a normal incident wall. The air attenuation is compensated by an amplifier whose gain increases with the time (range)
\
5
~
4
3 2
0 0
7. SIMULATION RESULTS
\
6
10
15
20
25
Fig 3 The ACF of a 4-bits PN code
139
Fig 4 Received signal with no noise. It illustrates a response of the sensor by using the barker code
Fig. 7. Experimental bench 8. EXPERIMENTAL VERIFICATION OF TOF
ESTIMATION
4(Il)
_
corrected TOF =true TOF
DD jy(t)1 200J
J
1(0)
0 0
200
~
A practical experiment has been carried out to verify the optimal filtering method. The components of the experiment are shown in figure 7. A Polaroid transducer which acts as emitter as well as receiver, is mounted on a driven azimuth scanning bench.
~ ./~- old TOF 600
1000
IOl
Fig. 5. The result of the correlation between the input (Barker code) and the received signal.
An interface card manages the emitted pulses. The reflected echo is detected by the receiver and digitised by a combiscope interacting with the PC, and operating at 200 Khz sampling rate (5 J-ls). The Polaroid driver electronics is simplified in order to transmit only binary signals fig 8.
In practice because of the thresholding, some periods of weaker received signals are lost. This introduced error is corrected by using a correlator. To verify this, the leading part of the received signal in figure 4 is suppressed (wrong estimation of T -O-F). After correlation, the output filtered is obtained in figure 5, and the true value of TOF is found. When noise is added in the simulation with SNR equal to 1, in the same conditions, optimum noise rejection is achieved (fig 6) and the output of the matched filter is the same as in figure 5. The result is close to an ideal sensor (Table I) Table 1 True value: z=1500 mm
T
modulated code code generator I and modulation
I
I I
PC
+160 VDC
Driverfor
I
~
~.J0,1
'--_se_n_or_---'I n
I ~' Amplifier
'--_ _ _-',
,
!
stage
U iT I
U '
"-J
I I
Transducer
-lr
estimation method_........._................. estimated distance .................... _.. __............................ _......... _.. _.. __ .................. _........ simple thresholding 1515.2 mm correlation 1500 mm
Received signal Fig. 8 Transmitting and receiving Electronics
~)~~ o
100 200 3J) ~ Th.t received ~ wiI:b. lID addil:ige noise
500
~~,~ I ": .~~I.~~~uJ The 61tered output of r(t)
Fig 9 Received signal coded by a 13-bits Barker code
Fig.6 The result of the correlation when SNR=1
140
10'r--~--~--------'
9 8
7
6
~
5 4
3 2
Fig 10 The output filtered corresponding to the received signal in fig 9
Figure 11 The filtered output It is important to notice that the real sensor under
A 13- bits Barker code modulates a 50 Khz carrier signal (PSK). The system is programmed to take measured range data by scanning a flat wall ahead of it.
practical condition is apparently noisier in the second case than the simulation conditions. So the peak/side lobe ratio is 9.52/1 probably due to the finite bandwidth of the transducer. To illustrate the advantage of using a Barker code, the transmit signal is replaced by a square signal (with a period of 20 ~s and Ims duration). The comparison between figure 11 and figure 10 explains why the resolution of the distance is better in the Barker code.
To compare the optimal method and the thresholding method of estimating the TOF the sensor is placed at 8=0° and z=1000 mm. In the case of the correlation method, the received signal is given in figure 9. Figure 10 illustrates the output after optimal filtering. Note in table 2, that the bias due to the thresholding method is not very important.
9. CONCLUSION Simple threshold detection produces a bias in the TOF measurement. An estimation of TOF by an optimal method to eliminate the bias, has been developed. It is based on radar techniques. It requires the shape of a waveform of the received signal. To enhance the resolution of the sensor, the Barker code is used for transmission. It is characterised by a short binary code and an auto correlation function close to the Dirac pulse. Simulation results show the principle of the correlation and experiment results illustrate the improvement of the resolution given by optimal filtering.
Another experiment is done at range z= 1000 mm and 8= 10°. In this case the SNR equals 3 instead of 87 in the previous case. With the thresholding method there is an important bias due the weak SNR, however with the optimal method the value of the true TOF is practically found, this result is illustrated in table 3. The real maximum of output will be located somewhere between two samples. Thus the accuracy of the range is limited to the gap between two samples (i.e. 0.859 mm at Ts=5 ~s) .
A hardware implementation of the correlator is in progress by using the DSP technology. That will allow the measurement of the estimator accuracy by computing the standard deviation of the estimates as functions of range and orientation. Also it might be interesting to generalise this study to obstacles like cylinders and angles and then try to extract their features .
Table 2 true value: TOF=5 .8224 ms, z=l m Method
TOF estimation
distance error
Optimal
5.825 ms
O.446mm
"'Thf~shoi~g-'-'5~835'~s'-"-""""""""'i":"i64'~""-"""""
Table 3 true value: TOF=5.8224 ms, z=l m Method
TOF estimation
distance error
Optimal
5.820 ms
0.42 mm
" 'T"~e'sh~i"d';;:;g'-'--5:'92S'~s"''''''''''''''-'''''''1"7:62'' mm''
.............
REFERENCES Audenaert, K. , H. Peremans, Y. Kawahara, and 1. Van Campenhout (1992). Accurate ranging of multiple objects using ultrasonic sensors. IEEE Transactions 0/1 Robotics and Automation pp. 1733-1738.
141
Barshan, B. and R Kuc (1992). A bat-like sonar system for obstacle localization. IEEE Transactions on systems, man, and cybernetics, Vol. 22. Berkowitz, R S (1965). Modern radar: analysis, evaluation and system design. ( John Wiley and Sons, Ed.), New-York. Biber, C., S. Ellin, E. Sheck and 1. Stempeck (1990). The Polaroid ultrasonic ranging system. In: proc. 67th Engineering Soc. Convention., (Reprinted in Polaroid mtrasonic Ranging System and Handbook) Bull, DR and S.M Thomas (1992). Ultrasonic ranging devices. (GB) British Nuclear Fuels PLC, Warrington; University College Cardiff Consultants LlD. Brevet. Elfes, R A (1985). Detection and classification phenomena of biological systems. In: Adaptive methods underwater Acoustics (H. G. Urban, Ed.), pp. 537-545. D. Reidel, New York. Hamadene, H . and E. Colle (I 996a). Methode suboptimale pour la localisation d'obstacles par tel6netrie ultrasonore. In GDR-PRC ISIS en fusion d'injormation ,Paris. Hamadene, H. and E. Colle (1996b). A method based on neural networks for the recognition of the environment scanned by ultrasonic sensor. EUFIT96, Vol. I, pp. 247-252. Aachen. Kuc, R and M.W. Siegel (1987). Physically-based simulation model for acoustic sensor robot navigation. IEEE Trans. Pattern Analysis and Machine Intelligent, Vol. 9, pp. 766-778. Polaroid corporation (1984). Ultrasonic ranging Systems, manual + handbook. Peremans, H ., K. Audenaert, and J. Van Carnpenhout (1993). A high-resolution sensor based on triaural perception. IEEE Transactions on Robotics and Automation, Vol. 9.
142
OPTIMAL ESTIMATION OF THE RANGE FOR MOBILE ROBOTS USING ULTRASONIC SENSORS
H. Hamadene and E. CoDe
CEMIF systemes complexes 40, rue du Pelvoux 91020 Evry Cedex hamadene@Cemifuniv-evryjr
Abstract: The measure of the range by an ultrasonic system is based on the measurement of the Time Of Flight (TOF) of an ultrasonic wave between a transmitter and a receiver. According to the signal-to-noise ratio, the TOF accuracy and the range accuracy will depend on the estimation method of the TOF. Three approaches can b~ used according to the complexity : thresholding, suboptimal method and correlation. The correlation method and its ~plementation are described. Simulation and experimental results.
detecting echoes in the received signal the distance between the transducer and the target can be found. But with conventional ultrasonic sensors (Audenaert, et al., 1992), some disadvantages appear because the measured distance depends on amplitude of the echo. Thus weaker echoes will be detected at a later time than stronger ones. This problem can be overcame by using some radar techniques (Berkowitz, 1965). It consists in: - having the estimated distance independent of the echo amplitude. - using an optimal filter in order to optimize the signal-to-noise ratio. - choosing the emitted signal to optimize the resolution.
I . INTRODUCTION
To move in an unknown environment, mobile robots need information given by exteroceptive sensors. The cost and the easiness of implementation explain the great use of ultrasonic sensors to provide range data. But the medium range accuracy and the wide beam complicate the environment recognition. The improvement of recognition ability requires a more accurate range measure. The paper focuses on the contribution of the correlation to the improvement of ultrasonic sensor range accuracy. After introducing briefly optimal filter theory and the three methods of TOF estimation., the corrdator is described. One of the most important point concerns the transmitted signal waveform. The results of simulations and experiments show the advantages of that optimal method compared to the usual thresholding.
The sensor-environment model adopted is the Kuc model (1994) which assumes that a process is linear and the received signal is expressed by r(/)
2. THEORY
=J[htr / ree (t)* helTVlr. (t)] . x(t -
,)d,
r(/ ) = J(htr / ree(t)* x(t)] . henvir(t - ,)dr
r(t) = Jxe(t)ehl /Vir . (t - r)dr (I)
Generally the ultrasonic transducer acts as both transmitter and receiver. It emits a burst of a certain fixed frequency (50 Khz in general which corresponds to the resonance frequency of the transducer), and by 137
Thus the output signal may (Audenaert, et al., 1992) by:
be
3.2. Suboptimal method
represented
r(t)=a.xe(t)+n(t) (2)
For nearby objects, in a high signal-ta-noise ratio case, the time of flight must be estimated by faster methods. It consists in approximating the leading part of the received signal by a function such a parabola (Barshan and Kuc, 1992; Hamadene and Colle 1996a). This is an intermediate approach between the biased threshold and the optimum correlation estimator method described next.
where a is an amplitude factor, Xe(t) is the ultrasonic transmit wave and n(t) is the additive noise present in the signal. In radar theory a filtered signal which has an optimal signal-ta-noise ratio can be expressed by :
y(t) =Jr(t) . h(t - -r)(iT (3) where h(t) is the impulse response of the environment (see equation 1). Such a filter is called a matched filter and its output will be :
3.3. Optimum correlation method A bat echolocation has been anaIyzed by Elfes (1985), he applied optimum correlation detection for TOF binaural estimation and target location. This method employs a matched filter that contains a copy of the echo to determine its location in the observed signal. It is an unbiased estimator which maximises the signal-to noise ratio. However this procedure is time consuming.
where tF is the time of flight of the transmitted pulse, is the time for which the filtered signal y(t) has the largest signal-to noise ratio of all linear filters, and Rx(t) is the autocorrelation function of x(t). By searching the maximum of y(t), the time-of-flight is carried out first and then the distance between the sensor and the target. t~
4. CORRELATOR IMPLEMENTATION 3." TIME-OF-FLIGHT ESTIMATION
The correlator is a digital matched filter in which the correlation is applied essentially between the input (transmitted wave) and the output (reflected wave) fig 1. The received signal is amplified before correlation and then correlated as follow :
The sensor operates in the pulse/echo mode, and acts as both a transmitter and a receiver. The echo reflected from an object may be detected by the same sensor now working as a receiver. Because of the addition of noise to the echoes detected, the TOF needs to be estimated. Three different methods of TOF estimation are presented.
y('t) =
KT
ex•r('t) = -ToJxe(t)·r(t)dt
(6)
where k is an amplification factor and T the duration of the calculus The matched filter can be approximated by a digital finite impulse response (7). The samples are multiplied by coefficients representing discrete samples of the 'reference signal' which is the transmit signal in our case. A mathematical representation of the matched filtering operation is as follows.
3.1. Simple thresholding method The method most frequently used by conventional sensors and sonar ranging systems for extracting the TOF information is a simple thresholding detection (Biber, et al., 1990). The sensor provides a range value when the echo amplitude exceeds a prespecified threshold level 1: which is set according to the noise level cr in order to suppress spurious readings. The time at which the received signal crosses the threshold 1: is denoted by :
N
y(n) = I,xe(i)·r(n-i) (7) ;=0
Note that it is about the cross-correlation and not the autocorrelation function because of the deformations of the received signal due to the reflectors and the finite bandwidth of the transducer. Fig 1 Synoptic of the treatment
r(t)
nX!
L--_--..,~!
where tF is the true value of the TOF, 1: the threshold and !IQ the shape parameter of the envelope of the received signal. The problem inherent to this method is the estimator bias.
~
y(1:)=Cxr('t) ~----~y------~~
correlator
138
Thanks to the amplitude of the filtered output we can get two information: the range r , between the sensor and the object, and its orientation (Hamadene and Colle, 1996b). Some researches are done in the determination of the emitted signal in order to get the correlated output assimilated to the Dirac pulse. This method will enhance the resolution and the signal-to-noise ratio of the sensor.
The emitted signal x(t) is a PSK (phase-Shift Keying) modulation of the Barker code where the carrier is a square wave with a 50 Khz frequency. With the modulation, the maximum level of the spectrum is centered at 50 Khz, the resonance frequency of the transducer. The total length of the emitted signal is 1 ms (polaroid Corporation, 1984), the duration symbol T=4x20~s where 20~s is the period of the carrier signal. Therefore the number of bits in the code must be 13 and B={+I, +1, +1, +1, +1, -1, -1, +1, +1, -1, +1, -1, +1} (Audenaert, et al., 1992; Peremans, et al. 1993).
5. CHOICE OF THE TRANSMIT WAVEFORM It consists in determining a code for which the sequence is as short as possible and its autocorrelation function close to the Dirac pulse. In the following paragraph we describe two kinds of codes and argue ourcboice.
5.2. PNcode Let C={cl' ~, ... , cp } be a sequence of the PN code, this code can easily be obtained by shift registers. For N registers, for example, the sequence generated will have 2N_l values ci= ±1, and the duration signal is (2N_l)T, where T is the duration of each symbol (equation 8). Each ci is evaluated using a characteristic polynome P(x). N was chosen to be 4. By comparing these two codes, one verifies that the length signal in the Barker code is 13T when in PN code it is 15T, also the blind zone of the sensor will be reduced in the Barker code, and the peaklside lobe ratio is 1311 in the Barker code when it is only 8/2 in PN codes figure 2 and figure 3.
5. J Barker code Let B={b l , b 2, .. ,bj, ..,bn } be an n-bits codeword with bi = ±l. From each bit hi a signal waveform can be derived by modulating a carrier signal xb(t) with the respective bi . For each bit bi corresponds a part of the signal x(t), called a symbol.
x(t+(i-l)1)=bi ·xb (t), t E[O,T] (8) where T is the duration of each symbol. 14r--~--~-~--~-----,
12
6. PEAK DETECTION 10
When an object is present in the active region of the ultrasonic range finder, the sensor will receive an echo. The received signal is sampled and converted with a 8 bits AID converter, the sampling period Ts=TC/4=5~s, where Tc is the period of the carrier signal.
4
:-----7-5 ---:'.:10,----~15;:----.:20:";:-----:!25
-20
The numerical received signal is correlated with the transmitted one. Then an evaluation of the absolute value of the filtered signal is made. The determination of the maximum provides the time of flight.
Fig 2 The Auto Correlation Function (ACF) of a 13-bits Barker code 8 7
The estimated results are obtained by simulating the ultrasonic sensors with a physically based model (Kuc and Siege~ 1987) that describes the transducer reflections from plans and corners. The TIR radius is chosen to be 15 mm, identical to the Polaroid transducer. The threshold level is chosen relatively to the amplitude of the echo from a normal incident wall. The air attenuation is compensated by an amplifier whose gain increases with the time (range)
\
5
~
4
3 2
0 0
7. SIMULATION RESULTS
\
6
10
15
20
25
Fig 3 The ACF of a 4-bits PN code
139
Fig 4 Received signal with no noise. It illustrates a response of the sensor by using the barker code
Fig. 7. Experimental bench 8. EXPERIMENTAL VERIFICATION OF TOF
ESTIMATION
4(Il)
_
corrected TOF =true TOF
DD jy(t)1 200J
J
1(0)
0 0
200
~
A practical experiment has been carried out to verify the optimal filtering method. The components of the experiment are shown in figure 7. A Polaroid transducer which acts as emitter as well as receiver, is mounted on a driven azimuth scanning bench.
~ ./~- old TOF 600
1000
IOl
Fig. 5. The result of the correlation between the input (Barker code) and the received signal.
An interface card manages the emitted pulses. The reflected echo is detected by the receiver and digitised by a combiscope interacting with the PC, and operating at 200 Khz sampling rate (5 J-ls). The Polaroid driver electronics is simplified in order to transmit only binary signals fig 8.
In practice because of the thresholding, some periods of weaker received signals are lost. This introduced error is corrected by using a correlator. To verify this, the leading part of the received signal in figure 4 is suppressed (wrong estimation of T -O-F). After correlation, the output filtered is obtained in figure 5, and the true value of TOF is found. When noise is added in the simulation with SNR equal to 1, in the same conditions, optimum noise rejection is achieved (fig 6) and the output of the matched filter is the same as in figure 5. The result is close to an ideal sensor (Table I) Table 1 True value: z=1500 mm
T
modulated code code generator I and modulation
I
I I
PC
+160 VDC
Driverfor
I
~
~.J0,1
'--_se_n_or_---'I n
I ~' Amplifier
'--_ _ _-',
,
!
stage
U iT I
U '
"-J
I I
Transducer
-lr
estimation method_........._................. estimated distance .................... _.. __............................ _......... _.. _.. __ .................. _........ simple thresholding 1515.2 mm correlation 1500 mm
Received signal Fig. 8 Transmitting and receiving Electronics
~)~~ o
100 200 3J) ~ Th.t received ~ wiI:b. lID addil:ige noise
500
~~,~ I ": .~~I.~~~uJ The 61tered output of r(t)
Fig 9 Received signal coded by a 13-bits Barker code
Fig.6 The result of the correlation when SNR=1
140
10'r--~--~--------'
9 8
7
6
~
5 4
3 2
Fig 10 The output filtered corresponding to the received signal in fig 9
Figure 11 The filtered output It is important to notice that the real sensor under
A 13- bits Barker code modulates a 50 Khz carrier signal (PSK). The system is programmed to take measured range data by scanning a flat wall ahead of it.
practical condition is apparently noisier in the second case than the simulation conditions. So the peak/side lobe ratio is 9.52/1 probably due to the finite bandwidth of the transducer. To illustrate the advantage of using a Barker code, the transmit signal is replaced by a square signal (with a period of 20 ~s and Ims duration). The comparison between figure 11 and figure 10 explains why the resolution of the distance is better in the Barker code.
To compare the optimal method and the thresholding method of estimating the TOF the sensor is placed at 8=0° and z=1000 mm. In the case of the correlation method, the received signal is given in figure 9. Figure 10 illustrates the output after optimal filtering. Note in table 2, that the bias due to the thresholding method is not very important.
9. CONCLUSION Simple threshold detection produces a bias in the TOF measurement. An estimation of TOF by an optimal method to eliminate the bias, has been developed. It is based on radar techniques. It requires the shape of a waveform of the received signal. To enhance the resolution of the sensor, the Barker code is used for transmission. It is characterised by a short binary code and an auto correlation function close to the Dirac pulse. Simulation results show the principle of the correlation and experiment results illustrate the improvement of the resolution given by optimal filtering.
Another experiment is done at range z= 1000 mm and 8= 10°. In this case the SNR equals 3 instead of 87 in the previous case. With the thresholding method there is an important bias due the weak SNR, however with the optimal method the value of the true TOF is practically found, this result is illustrated in table 3. The real maximum of output will be located somewhere between two samples. Thus the accuracy of the range is limited to the gap between two samples (i.e. 0.859 mm at Ts=5 ~s) .
A hardware implementation of the correlator is in progress by using the DSP technology. That will allow the measurement of the estimator accuracy by computing the standard deviation of the estimates as functions of range and orientation. Also it might be interesting to generalise this study to obstacles like cylinders and angles and then try to extract their features .
Table 2 true value: TOF=5 .8224 ms, z=l m Method
TOF estimation
distance error
Optimal
5.825 ms
O.446mm
"'Thf~shoi~g-'-'5~835'~s'-"-""""""""'i":"i64'~""-"""""
Table 3 true value: TOF=5.8224 ms, z=l m Method
TOF estimation
distance error
Optimal
5.820 ms
0.42 mm
" 'T"~e'sh~i"d';;:;g'-'--5:'92S'~s"''''''''''''''-'''''''1"7:62'' mm''
.............
REFERENCES Audenaert, K. , H. Peremans, Y. Kawahara, and 1. Van Campenhout (1992). Accurate ranging of multiple objects using ultrasonic sensors. IEEE Transactions 0/1 Robotics and Automation pp. 1733-1738.
141
Barshan, B. and R Kuc (1992). A bat-like sonar system for obstacle localization. IEEE Transactions on systems, man, and cybernetics, Vol. 22. Berkowitz, R S (1965). Modern radar: analysis, evaluation and system design. ( John Wiley and Sons, Ed.), New-York. Biber, C., S. Ellin, E. Sheck and 1. Stempeck (1990). The Polaroid ultrasonic ranging system. In: proc. 67th Engineering Soc. Convention., (Reprinted in Polaroid mtrasonic Ranging System and Handbook) Bull, DR and S.M Thomas (1992). Ultrasonic ranging devices. (GB) British Nuclear Fuels PLC, Warrington; University College Cardiff Consultants LlD. Brevet. Elfes, R A (1985). Detection and classification phenomena of biological systems. In: Adaptive methods underwater Acoustics (H. G. Urban, Ed.), pp. 537-545. D. Reidel, New York. Hamadene, H . and E. Colle (I 996a). Methode suboptimale pour la localisation d'obstacles par tel6netrie ultrasonore. In GDR-PRC ISIS en fusion d'injormation ,Paris. Hamadene, H. and E. Colle (1996b). A method based on neural networks for the recognition of the environment scanned by ultrasonic sensor. EUFIT96, Vol. I, pp. 247-252. Aachen. Kuc, R and M.W. Siegel (1987). Physically-based simulation model for acoustic sensor robot navigation. IEEE Trans. Pattern Analysis and Machine Intelligent, Vol. 9, pp. 766-778. Polaroid corporation (1984). Ultrasonic ranging Systems, manual + handbook. Peremans, H ., K. Audenaert, and J. Van Carnpenhout (1993). A high-resolution sensor based on triaural perception. IEEE Transactions on Robotics and Automation, Vol. 9.
142